Encoding a qubit into an oscillator for protection and force sensing
In 2000 Gottesman, Kitaev and Preskil formulated a proposal to encode
a qubit in an oscillator (e.g. a cavity mode). Until last year no
reasonable preparation scheme for such highly non-classical 'grid'
states was known. We show how the preparation of a grid state could be
realized using a dispersive cavity-qubit coupling, similar to the
creation of Schrödinger cat states in superconducting microwave
cavities in circuit-QED. The essence of the preparation protocol is to
do phase estimation for a unitary displacement operator. We also show
why an oscillator grid state can be useful for displacement or force
sensing. Preparing the oscillator in such state allows one to
determine both parameters of a displacement with an accuracy which
scales inversely with the square root of the number of photons in the
oscillator. For squeezed or coherent states this accuracy is always at
least a constant, independent of photon number.